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Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of…
For a subset $B$ of $\mathbb{R}$, denote by $\operatorname{U}(B)$ be the semiring of (univariate) polynomials in $\mathbb{R}[X]$ that are strictly positive on $B$. Let $\mathbb{N}[X]$ be the semiring of (univariate) polynomials with…
A semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities having real coefficients and is a union of finitely many maximally connected components. We consider the problem of deciding whether two…
Many empirical studies have provided evidence for the emergence of algorithmic mechanisms (abilities) in the learning of language models, that lead to qualitative improvements of the model capabilities. Yet, a theoretical characterization…
Large Language Models (LLMs) struggle with complex reasoning due to limited diversity and inefficient search. We propose Soft Reasoning, an embedding-based search framework that optimises the embedding of the first token to guide…
To assist non-specialists in formulating database queries, multiple frameworks that automatically infer queries from a set of examples have been proposed. While highly useful, a shortcoming of the approach is that if users can only provide…
The question of how to certify the non-negativity of a polynomial function lies at the heart of Real Algebra and it also has important applications to Optimization. In the setting of symmetric polynomials Timofte provided a useful way of…
Recent advancements in Large Language Models (LLMs) have demonstrated remarkable capabilities in various domains. However, effective decision-making relies heavily on strong reasoning abilities. Reasoning is the foundation for…
Recent studies on reasoning in language models (LMs) have sparked a debate on whether they can learn systematic inferential principles or merely exploit superficial patterns in the training data. To understand and uncover the mechanisms…
Grounding large language models (LLMs) in external knowledge sources is a promising method for faithful prediction. While existing grounding approaches work well for simple queries, many real-world information needs require synthesizing…
In modern machine learning, pattern recognition replaces realtime semantic reasoning. The mapping from input to output is learned with fixed semantics by training outcomes deliberately. This is an expensive and static approach which depends…
We address the problem of propositional logic-based abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based…
Explainable Artificial Intelligence and Formal Argumentation have received significant attention in recent years. Argumentation-based systems often lack explainability while supporting decision-making processes. Counterfactual and…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
Monotone frameworks is one of the most successful frameworks for intraprocedural data flow analysis extending the traditional class of bitvector frameworks (like live variables and available expressions). Weighted pushdown systems is…
For every group $G$, the set $\mathcal{P}(G)$ of its subsets forms a semiring under set-theoretical union $\cup$ and element-wise multiplication $\cdot$ and forms an involution semigroup under $\cdot$ and element-wise inversion ${}^{-1}$.…
Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
Neural language models are a powerful tool to embed words into semantic vector spaces. However, learning such models generally relies on the availability of abundant and diverse training examples. In highly specialised domains this…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…